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Answer :
The maximum work required by the machine is 16420 J.
What is work?
Work is energy transferred to or from an object via the application of the force along with the displacement. Work is the standard mechanical quantity. In its simple form, for a constant force aligned with it direction of motions the work equals the product of the forced by the strength and to the distance traveled.
Here mass M is 215 kg
And the height lifted H is 5.65
The energy or workdone needed to lift is W= MgH = 215(9.8)(5.65)= 11904.5 J
The minimum efficiency of to the machine is 72.5 %
So we can write that
The workdone by machine is
11904.5(100/72.5) = 16420 J ( approx)
So the workdone by machine is 16420 J
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Final answer:
To lift a 215 kg mass 5.65 m using a machine that is 72.5% efficient, the actual work required is calculated to be approximately 16486.5 Joules, taking into account the machine's efficiency.
Explanation:
To calculate the work required to lift a 215 kg mass a distance of 5.65 m using a machine that is 72.5% efficient, we first need to find the ideal work done, which is the work that would be required if the machine were 100% efficient. The formula for work (Work) when lifting an object is given by:
Work = mass × gravitational acceleration × height
Using a gravitational acceleration of 9.8 m/s², the ideal work can be calculated as:
Work = 215 kg × 9.8 m/s² × 5.65 m
Doing the calculation:
Work = 11952.7 J (Joules, rounded to one decimal place)
However, since the machine is only 72.5% efficient, the actual work done by the machine is higher than the ideal work. The actual work can be found by dividing the ideal work by the efficiency (expressed as a decimal).
Actual Work = Ideal Work / Efficiency
In this case:
Actual Work = 11952.7 J / 0.725
So the actual work required by the machine is:
Actual Work = 16486.5 J (Joules, rounded to one decimal place)
